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Relative Derived Delooping Levels and τ-Tilting Modules
Abstract
Let ℰ be an essentially small idempotent-complete exact category with enough projective objects. We develop derived delooping levels in ℰ. We apply this framework to a basic support τ-tilting module T. We then define the derived delooping level relative to T and compare it with the ordinary relative delooping level and the derived delooping level of B=EndA(T). We show that the big finitistic dimension of Bop is bounded above by the derived delooping level of FacT relative to T. Moreover, we prove that a self-orthogonal τ-tilting module T is a $1$-tilting module whenever 2−ddellB(DT) is finite.
Related
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- Derived Delooping Levels of One-Point Extensions and Finitistic Dimensions
- Reduction techniques for the derived delooping levels
BibTeX
@misc{gao2026relative,
title = {{Relative Derived Delooping Levels and $τ$-Tilting Modules}},
author = {Hanpeng Gao and Dajun Liu and Houjun Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39011},
eprint = {2609.39011},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39011},
}
RIS
TY - UNPB
TI - Relative Derived Delooping Levels and τ-Tilting Modules
AU - Hanpeng Gao
AU - Dajun Liu
AU - Houjun Zhang
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39011
UR - https://arxiv.org/abs/2609.39011
AB - Let ℰ be an essentially small idempotent-complete exact category with enough projective objects. We develop derived delooping levels in ℰ. We apply this framework to a basic support τ-tilting module T. We then define the derived delooping level relative to T and compare it with the ordinary relative delooping level and the derived delooping level of B=End_A(T). We show that the big finitistic dimension of B^op is bounded above by the derived delooping level of FacT relative to T. Moreover, we prove that a self-orthogonal τ-tilting module T is a $1$-tilting module whenever 2−ddell_B(DT) is finite.
ER -